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COMP 538 Reasoning and Decision under Uncertainty Introduction Readings: Pearl (1998, Chapter 1 Shafer and Pearl, Chapter 1 COMP 538 Introduction / Slide 2 Objectives Course objectives Course contents COMP 538 Introduction / Slide 3 Uncertainty Uncertainty: the quality or state of being not clearly known. Uncertainty appears in many tasks Partial knowledge of the state of the world Noisy observations Phenomena that is not covered by our models Inherent randomness COMP 538 Introduction / Slide 4 Probability and Decision Theory Well-known and well-understood framework for uncertainty Clear semantics Provides principled answers for: Combining evidence Predictive & Diagnostic reasoning Incorporation of new evidence Intuitive (at some level) to human experts Can be learned COMP 538 Introduction / Slide 5 Course Objectives When applied to real-world problems, probability theory and decision theory suffer from Complexity of model construction Complexity of problem solving This course covers methodologies developed recently in AI community for dealing with those complexity problems. The methodologies combine ideas from several disciplines Artificial Intelligence, Machine Learning Decision Theory, Theory of Computer Science Statistics, Information Theory, Operations Research COMP 538 Introduction / Slide 6 Complexity Problem of Applying Probability Theory Example: Patients in hospital are described by several attributes: Background: age, gender, history of diseases, … Symptoms: fever, blood pressure, headache, … Diseases: pneumonia, heart attack, … A joint probability distribution needs to assign a number to each combination of values of these attributes, exponential model size. 20 attributes require 2020 ( roughly 106 ) numbers Real applications usually involve hundreds of attributes COMP 538 Introduction / Slide 7 Complexity Problem of Applying Probability Theory Because of the exponential model size problem, it was believed that probability theory is not practical for dealing with uncertainty in AI. Alternative uncertainty calculi were introduced: uncertainty factors, non-monotonic logic, fuzzy logic, etc. COMP 538 Introduction / Slide 8 Complexity Problem of Applying Probability Theory Bayesian networks alleviate the exponential model size problem. Key idea: use conditional independence to factorize model into smaller parts. MINVOLSET Example: Alarm network PULMEMBOLUS INTUBATION KINKEDTUBE VENTMACH DISCONNECT 37 variables PAP SHUNT VENTLUNG VENITUBE 237 Model size: Size of factored model: 509 PRESS MINOVL ANAPHYLAXIS Model construction and problem solving becomes possible SAO2 TPR HYPOVOLEMIA LVEDVOLUME CVP PCWP LVFAILURE STROEVOLUME FIO2 VENTALV PVSAT ARTCO2 INSUFFANESTH CATECHOL HISTORY ERRBLOWOUTPUT CO HR HREKG HRBP BP EXPCO2 ERRCAUTER HRSAT COMP 538 Introduction / Slide 9 Advantages of Bayesian Networks Semantics Model construction by expert Probability theory provides the glue whereby the parts are combined, ensuring that the system as a whole is consistent. Alternative approaches suffer from several semantic deficiencies (Pearl 1988, Chapter 1). Appealing graphical interface allows experts to build model for highly interacting variables. Model construction from data Probability foundation allows model construction from data by well established statistical principles such as maximum likelihood estimation and Bayesian estimation. COMP 538 Introduction / Slide 10 Fielded Applications Expert systems Monitoring Space shuttle engines (Vista project) Freeway traffic Sequence analysis and classification Medical diagnosis Fault diagnosis (jet-engines, Windows 98) Speech recognition Biological sequences Information access Collaborative filtering Information retrieval See tutorial by Breese and Koller (1997) and online resources for application samples. COMP 538 Introduction / Slide 11 Course Content/Bayesian Networks Concept and semantics of Bayesian networks Inference: How to answer queries efficiently Learning: How to learn/adapt Bayesian network models from data Causal models: How to learn causality from statistical data Detailed discussion of those topics can take one whole course (DUKE). We will focus on the main ideas and skip the details so that we can study other related topics. COMP 538 Introduction / Slide 12 Bayesian networks and classical multivariate models Special cases of Bayesian networks: many of the classical multivariate models from statistics, systems engineering, information theory, pattern recognition and statistical mechanics Examples: mixture models, factor analysis, hidden Markov models, Kalman filters, Ising models. Bayesian networks provide a way to view all of these models as instances of a common underlying formalism. COMP 538 Introduction / Slide 13 Course Content/Special models Latent class analysis: Statistical method for finding subtypes of related cases. With proper generalization, might provide a statistical foundation for Chinese medicine diagnosis. Hidden Markov models: A temporal model widely used in pattern recognition: handwriting recognition, speech recognition. COMP 538 Introduction / Slide 14 Decision Making under Uncertainty Typical scenario: whether to take umbrella Decision theory provides basis for rational decision making: Maximum expected utility principle. Decision analysis: applying of decision theory. Suffers from exponential model size. COMP 538 Introduction / Slide 15 Course Content/Simple Decision Making Influence diagrams Generalization of Bayesian network. Alleviate the complexity problem of decision analysis Topics: Evaluation: How to compute optimal decisions in an influence diagram. Value of information: Whether it is worthwhile to collect more information to reduce uncertainty. COMP 538 Introduction / Slide 16 Sequential Decision Making under Uncertainty Agent/robot needs to execute multiple actions in order to achieve a goal Uncertainty originates from noisy sensor and inaccurate actuators/uncontrollable enviroment factors What is the best way to reach goal with minimum cost/time? COMP 538 Introduction / Slide 17 Course Content/Sequential Decision Making Models: Markov decision processes, consider only uncertainty in actuators/environment factors Partially observable decision processes, consider uncertainty in sensors and actuators/environment factors. Solution methods: Value iteration Policy iteration Dealing with model complexity using dynamic Bayesian networks Learning sequential decision models Model-based reinforcement learning COMP 538 Introduction / Slide 18 Course Content/Summary Bayesian networks Concept and semantics, inference, learning, causilty Special models: Hidden Markov models, latent class analysis Influence diagrams: Evaluation, value of information Markov decision processes and partially observable Markov decision processes Solution methods: value iteration, policy iteration, dynamic Bayesian networks Model-based reinforcement learning